OAE Mathematics flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Rational number

A number expressible as a ratio of two integers with a nonzero denominator; its decimal form terminates or eventually repeats.

Divisibility rule for 9

A whole number is divisible by 9 exactly when the sum of its digits is divisible by 9; the same test with 3 works for divisibility by 3.

Absolute value as distance

|a − b| gives the distance between a and b on the number line, so |x| = 5 has solutions x = 5 and x = −5.

Percent change formula

Percent change equals (new value minus old value) divided by old value, then multiplied by 100; a positive result is an increase.

Slope formula

For two points, slope m = (y_2 − y_1)/(x_2 − x_1); it measures vertical change per unit of horizontal change and is undefined for vertical lines.

Quadratic discriminant

For y = ax² + bx + c, the discriminant b² − 4ac gives two real roots when positive, one when zero, and none when negative.

Arithmetic sequence formula

The nth term is a_n = a_1 + (n − 1)d, where a_1 is the first term and d is the constant common difference between consecutive terms.

Inverse function property

If f and f⁻¹ are inverses, then f(f⁻¹(x)) = x and their graphs are mirror images across the line y = x.

Pythagorean theorem

In a right triangle, a² + b² = c² where c is the hypotenuse; the converse proves a triangle is right when the equation holds.

Similar figure area ratio

When two figures are similar with scale factor k, their areas compare as k² and their volumes compare as k³.

Circle area and circumference

A circle of radius r has circumference C = 2πr and area A = πr²; diameter equals twice the radius.

Interior angle sum

The interior angles of a polygon with n sides sum to (n − 2)·180 degrees, so a quadrilateral totals 360 degrees.

Cylinder volume and surface area

A cylinder of radius r and height h has volume V = πr²h and total surface area 2πr² + 2πrh, including both circular bases.

Combination formula

C(n, r) = n!/(r!(n − r)!) counts unordered selections of r items from n; order does not matter, unlike permutations.

Addition rule of probability

P(A or B) = P(A) + P(B) − P(A and B); the subtraction removes outcomes counted in both events.

Expected value

Expected value is the sum of each outcome's value multiplied by its probability, giving the long-run average result of repeated trials.

Independent events

Two events are independent when P(A and B) = P(A)·P(B); knowing one occurred does not change the probability of the other.

Binomial probability

The probability of exactly k successes in n independent trials is C(n, k)·p^k·(1 − p)^(n − k), where p is the success probability.

Euler circuit condition

A connected graph has an Euler circuit that uses every edge once exactly when every vertex has even degree.

Scientific notation

A number is written as a × 10^n with 1 ≤ |a| < 10; multiplying such numbers adds exponents, and dividing subtracts them.

Greatest common factor

The GCF is the product of the shared prime factors raised to their lowest common powers; the LCM uses the highest powers.

Zero product property

If a product equals zero, then at least one factor equals zero; this solves factored equations such as (x − 3)(x + 5) = 0.

Vertical line test

A graph represents a function only if no vertical line crosses it more than once, meaning each input has exactly one output.

Exponential growth form

Exponential growth or decay follows y = a·b^x, with b > 1 for growth and 0 < b < 1 for decay, and a as the initial value.

Triangle congruence criteria

SSS, SAS, ASA, AAS, and HL establish congruence; AAA establishes only similarity because side lengths may differ.

Inscribed angle theorem

An inscribed angle measures half its intercepted arc, while a central angle measures the full arc it intercepts.

Special right triangle ratios

A 45-45-90 triangle has sides in ratio 1:1:√2; a 30-60-90 triangle has sides in ratio 1:√3:2.

Interquartile range

IQR = Q3 − Q1, the spread of the middle half of the data; it resists outliers better than the range.

Correlation coefficient

The value r ranges from −1 to 1; values near ±1 indicate strong linear association, and zero indicates no linear association.

Recursive sequence rule

A recursive rule defines each term from earlier terms and requires a starting value, such as a_1 = 3 and a_n = 2a_(n−1).

Conditional probability formula

P(A|B) = P(A and B)/P(B), the probability of A given that B occurred; the denominator restricts the sample space to event B.

Distributive property

a(b + c) = ab + ac; multiplication distributes over addition and subtraction, allowing expressions to be expanded or factored.